From everything I've read about quantum mechanics and quantum entanglement phenomena, it's not obvious to me why quantum entanglement is considered to be an active link. That is, it's stated every time that measurement of one particle affects the other.

In my head, there is a less magic explanation: the entangling measurement affects both particles in a way which makes their states identical, though unknown. In this case measuring one particle will reveal information about state of the other, but without a magical instant modification of remote entangled particle.

Obviously, I'm not the only one who had this idea. What are the problems associated with this view, and why is the magic view preferred?

8 Answers
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Entanglement is being presented as an "active link" only because most people - including authors of popular (and sometimes even unpopular, using the very words of Sidney Coleman) books and articles - don't understand quantum mechanics. And they don't understand quantum mechanics because they don't want to believe that it is fundamentally correct: they always want to imagine that there is some classical physics beneath all the observations. But there's none.

You are absolutely correct that there is nothing active about the connection between the entangled particles. Entanglement is just a correlation - one that can potentially affect all combinations of quantities (that are expressed as operators, so the room for the size and types of correlations is greater than in classical physics). In all cases in the real world, however, the correlation between the particles originated from their common origin - some proximity that existed in the past.

People often say that there is something "active" because they imagine that there exists a real process known as the "collapse of the wave function". The measurement of one particle in the pair "causes" the wave function to collapse, which "actively" influences the other particle, too. The first observer who measures the first particle manages to "collapse" the other particle, too.

This picture is, of course, flawed. The wave function is not a real wave. It is just a collection of numbers whose only ability is to predict the probability of a phenomenon that may happen at some point in the future. The wave function remembers all the correlations - because for every combination of measurements of the entangled particles, quantum mechanics predicts some probability. But all these probabilities exist a moment before the measurement, too. When things are measured, one of the outcomes is just realized. To simplify our reasoning, we may forget about the possibilities that will no longer happen because we already know what happened with the first particle. But this step, in which the original overall probabilities for the second particle were replaced by the conditional probabilities that take the known outcome involving the first particle into account, is just a change of our knowledge - not a remote influence of one particle on the other. No information may ever be answered faster than light using entangled particles. Quantum field theory makes it easy to prove that the information cannot spread over spacelike separations - faster than light. An important fact in this reasoning is that the results of the correlated measurements are still random - we can't force the other particle to be measured "up" or "down" (and transmit information in this way) because we don't have this control even over our own particle (not even in principle: there are no hidden variables, the outcome is genuinely random according to the QM-predicted probabilities).

I recommend late Sidney Coleman's excellent lecture Quantum Mechanics In Your Face who discussed this and other conceptual issues of quantum mechanics and the question why people keep on saying silly things about it:

I wish to complete @Luboš Motl's answer, to which I agree. My point is on why people continue to make this mistake of an active link. This mistake is connected with one of the most interesting properties of quantum mechanics, Bell's theorem. One can argue that any physical theory is an hidden variable theory, the hidden variable being the description of the state of an object as written by the theoretician describing it. For quantum theory, the wavefunction of the object is the hidden variable.

Bell's theorem state that the prediction of quantum theory cannot be described by any local hidden variable theory. More precisely, for any entangled state, you can find a set of measurement with statistics contradicting any local hidden variable theory. The two possible explanations are either :

Nature is not local : your physical description is a real physical object, and there is an active non-local link between the two entangled particle.

Nature is not realist : your physical state is only an approximation and has no real meaning.

Nature is not quantum.

(1) is much easier to explain and appears often in popular science, mainly because (2) is much more difficult to explain and accept. But I think most researcher working with entanglement prefer explanation (2). Einstein intuition was 3 (before Bell's theorem), because he could not accept (1) and (2).

Interestingly, Einstein 1936 original paper on the EPR paradox was on a case where you can easily find a local hidden variable theory. The state described it what is now called a two-mode squeezed state. It's Wigner function is positive and can therefore be interpreted as a classical probability distribution on the quadrature (position and momentum) measurements, the only one discussed in the EPR paper. Such classical analysis of entanglement can be theoretically very useful and help the intuition in some case without needing any spooky action at distance. However, as shown by Bell, such local hidden variable theory cannot be generic enough to encompass all quantum mechanics.

This is a nice answer. I think, especially, it's good that you point out that when someone tells you to give up "local realism," the right answer is to give up the "realism" part. It's a bad choice of word anyway; the real world is quantum.
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Matt ReeceJan 21 '11 at 5:38

This is a good answer, just nit picking on one thing not being precise, in (2) you seem to be saying that the physical state has no real meaning because it is only approximate, implying a correctable technical problem. Maybe the thing to say is it has no meaning because it has redundant information? @Matt, I like your point, strange that "realism" in this debate came to refer to an intuitive but ultimately wrong view of the world, it's like hearing about the flogiston realism. Good catch.
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user566Jan 27 '11 at 15:30

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+1 a great answer, but one thing puzzles me (especially in conjunction with the answer by @Luboš): you state that the wave function is the non-local hidden variable which describes probabilities for the entangled particles, implying that the act of measurement does not actually influence the other particle, but merely unravels our knowledge about its state. Now, if this is not a local theory (not contradicting Bell's theorem), why do you state that one needs to conclude that nature is not realist and the physical state has no meaning?
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GrooJul 28 '14 at 8:38

In fact your view is quite close to the 'official' one; entanglement occurs just because both particles are described with one wave-function; the magic is in our classical habit of thinking that separate objects are described with separate "coordinates".

+1 well put. I think the main problem is that quantum mechanics still treats several instances of one particle kind with different wave functions, while quantum field theory kills a lot of that confusion
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Tobias KienzlerJan 17 '11 at 15:32

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@Tobias Kienzler: That doesn't help. You can have entanglement between non-identical particles just as easily. Having widely separated positions really is enough for the correlations of identical particles to work the same way.
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wnoiseDec 1 '11 at 16:26

@wnoise: true, though I think one can describe QFT by having a functional where the different particle fields are the "coordinates" (i.e. the particle fields themselves are "excitations" in that functional)
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Tobias KienzlerDec 16 '11 at 8:55

Imagine at home you put one glove in your coat without looking (and noticing it's only one of the two). After exiting the train you notice it's cold and you pull out that single glove. At this very instant you know it's either the left or the right glove, and you therefore know which one is left at home. However, no information was transmitted by your "measurement". Of course in quantum mechanics this is more complicated because of the not entirely measurable wave function, but this is the basic idea.

It's a little more complicated than the glove example, though, because the state of an entangled quantum system is indeterminate until the measurement is made, leading to stronger correlations than can be observed with a purely classical system like a pair of gloves. Bell's theorem shows that quantum systems can be correlated in ways that classical systems cannot, and that's a genuinely surprising result from the standpoint of classical intuition.
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Chad OrzelJan 17 '11 at 16:30

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@Chad: Isn't everything indeterminate until a measurement is made? If no one checks either the glove at home or the glove in your pocket, then it will remain unknown which one you have.
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JorenJan 17 '11 at 16:45

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The quantum indeterminacy is different than the classical "we don't know which glove in in your pocket" sort of uncertainty. If you reach into your pocket and pull out a left glove, you can be confident that it was the left glove when you put it there, and has been the left glove all along until you measured it. This is not the case with quantum entangled states. If you measure a photon to be vertically polarized, that does not mean it was vertically polarized when it left the source-- in fact, it can't have been vertically polarized, because that would be inconsistent with Bell's Theorem.
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Chad OrzelJan 17 '11 at 17:22

@Chad Orzel: that's true, I didn't want to go into detail too much. The basic problem is that the observer is still considered a classical system. Luboš' answer has the details. Basically there's a hen-egg problem that you measure yourself measuring and therefore perceive your own wavefunction collapsing in the state of having measured a collapsed state... kind of.
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Tobias KienzlerJan 18 '11 at 8:08

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+1. Sometimes precision is the enemy of pedagogy. The next time someone asks me about this kind of thing at a cocktail party, this is exactly the analogy I'll give. It all depends on the level of the audience.
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Ben CrowellApr 15 '13 at 0:35

I think that the best picture to understand this correlation is given by many-worlds interpretation:

A singlet decomposes in a coupled pair of particles superposition $|+⟩_A|-⟩_B + |-⟩_A|+⟩_B$, so observer A sees a simple superposition of $|+⟩ + |-⟩$ (which is a partial trace of the global density matrix) and so does B.

In the many worlds interpretation, observer A will be split in a $+$ and a $-$ observer (and so will observer B). Now, where will the correlation effect manifest itself?

The 'coupling' effect is brought when observer A and observer B join together at subluminal speeds to compare notes of their measurements: (remember that according to many-worlds, we have two observers A and two observers B) .

Observer A+ is disallowed by angular momentum conservation to interact with observer B+, (otherwise they will both agree that angular momentum was not conserved). Likewise, observer A- is disallowed to interact with observer B- by the same reason.

So the remaining interactions between observers are:

A+ interacts with B-

A- interacts with B+

so the final state is a superposition of $|+⟩_A|-⟩_B$ and $|-⟩_A|+⟩_B$, which is interpreted as a 'correlation between remote observations'.

This is incorrect. The partial trace over $B$ of $\rho=|\Psi⟩⟨\Psi|$, for $|\Psi⟩=(|+-⟩+|-+⟩)/\sqrt 2$, is the completely mixed state, which is an evenly weighted probabilistic mixture (and not a superposition) of the A states $|+⟩$ and $|-⟩$.
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Emilio PisantyNov 26 '14 at 13:37

it's unobvious for me, why quantum entanglement is considered to be active link

Let's walk through a particular variant of the EPR paradoxon. You probably already know this, but I don't know how to explain the problem any other way:

Consider a source that produces entangled photon pairs polarized in z-direction with net spin 0, and two physicists Alice and Bob making measurements.

Alice always measures the spin component of her photon in x-direction, whereas Bob may measure the spin component of his photon in either x- or y-direction.

Let's assume that the source, Alice and Bob are at rest relative to the lab frame, but Bob is closer to the source and makes his measurement first. If Bob takes a measurement in y-direction, Alice' measurements will be uncorrelated. If Bob takes a measurement in z-direction, results will be correlated: Alice will always measure the opposite spin.

This is paradoxical if you assume wave function collapse is real and local, however is happens (magic, decoherence, stochastic interactions or whatever else floats your boat).

Somehow, Bob's photon needs to tell its partner that it can do whatever it wants if the measurement was taken in y-direction, but force it to do the right thing if the measurement was taken in x-direction. This information needs to propagate faster-than-light so it's available before Alice makes her measurement.

There are several possible ways out of this situation, and I'll list three of them:

First, you can posit that there never was a collapse, that we're just dealing with statistical correlation and the paradox is a result of applying classical intuition to quantum systems.

Second, you can posit that the spooky action at a distance is time-symmetric, ie both Alice' and Bob's measurement will send information slower-than-light but backwards in time until it reaches the event that created the entanglement, which in turn sends information forwards in time. The photons will always have known what spin they'll need to end up with. The pseudo-time I used in my explanation is only a didactic tool: The physical process is atemporal interference across space-time.

Third, you can accept that there are indeed faster-than-light interactions, which, however, cannot be used to transmit information - they are an internal bookkeeping mechanism that keeps the universe in sync. The same thing happens in quantum field theory, which is explicit if you use the virtual particle picture, but even without it there are correlations between field excitations across space-like separation.

It is not really clear that cases 1,2, and 3 are exhaustive. Discussions
about this phenomenon use a lot of terms which are not precisely defined.
For example, 'particle' and 'system'. If there is entanglement, then
there is one combined system, and it is misleading to call that one combined
system 'two particles'.

The comment about realism and approximation is also inaccurate: all positions
and data in classical physics are approximate too, this has nothing to do
with the difference between classical and quantum or the difference betweeen
using a Hamiltonian system whose states are points given by momentum and
position coordinates and using a Hamiltonian system whose points are
rays in a Hilbert Space.

The comment about entanglement only originating from contiguity in the past
is inaccurate and even if true, proves nothing if the Big Bang is true,
then nothing prevents every part of the universe from being entangled, and
it probably is entangled, but in a way that has no practical importance.

People's comments here touch on the important issue of whether the wave
function is objective or subjective. The view that probabilities represent
our knowledge is called the 'Bayesian' view, it is the Bayesian or
subjective interpretation of probability, as contrasted to the 'objective
view' which has some problems. But the Bayesian view has problems as well,
since you wind up linking quantum mechanics with consciousness instead
of with material measuring apparati such as Geiger counters and bubble
chambers.

So another answer to your question is the following: people prefer
to talk about an active link because they cannot accept the subjective
interpretation of probability and the wave function. There is a lot of
current research studying quantum measurement as an actual physical
process involving thermodynamic limits of unstable negative temperature
systems (bubble chambers etc.).

To put this another way:

alternative 1 implicitly assumes that in the
combined system there are 'two particles', but this is probably a
fallacy: quantum mechanics does not really recognize any precise notion
of particle. As in thermodynamic limits, the notion of 'particle' is
a useful approximation within a certain range of set-ups, and loses
validity and leads to paradoxes if you attempt to use it outside
the limits of its validity.

Alternative 2 implicitly assumes that if something such
as the wave function can only be approximately measured, it is somehow
not 'physical', but this is unduly simplistic and troubles people
because of the seeming necessity of dragging in the subjective Bayesian
point of view.

Alternative 3 is at least so open ended that one cannot find
fault with it but neither is there a shred of experimental evidence for
it. The only problems with QM are logical, not experimental.

Therefore if one questions the implicit assumptions made
about the careless use of concepts such as 'particle', 'system', and
'probability', there are many more alternatives and the final answer is
not in.

Let's try to understand through Sock Physics. Suppose you have two socks, that obey classical physics laws and they are of different colours, now you take one of them without knowing and leave one of them home without knowing which one you took. Then when you were on a different planet, you decide to look. You find it is green and can infer that the other sock must be blue. Why ?
Because it's classical physics. You know that classical physics following objects behave like this through experience of classical physics.

Now, suppose there were two entangled socks that obeyed quantum physics laws. You measured one and could infer the other due to their entangled nature. Why ? Because they obey quantum laws. Quantum laws are stranger, but they tell you the outcome that occured. All the information transfer shit will come if you try to understand quantum laws through a classical picture.
In quantum laws, you've information transfer as well. It turns out you don't need it here.

And the rest is understood by Lubos Motl's answer . Why the wave function isn't a real wave and hence can travel faster than light in some cases and not in some other cases. Your real particles can't travel faster than light and the wave funciton evolution will adjust automatically according to the given constraints for that, in QFT not in non relativistic quantum mechanics.